The classical one-parameter, and the two-parameter Mittag-Leffler functions
are defined by [1]}:
\(\begin{array}{l}\displaystyle \mathrm {E}_{\alpha }\left( x\right) =\sum _{k=0}^{\infty }\frac{x^{k}}{\Gamma \left( \alpha k+1\right) },\quad \mathrm {Re}\,\alpha >0, \\\displaystyle \mathrm {E}_{\alpha ,\beta }\left( x\right) =\sum _{k=0}^{\infty }\frac{x^{k}}{\Gamma \left( \alpha k+\beta \right) },\quad \mathrm {Re}\,\alpha >0,\ \mathrm {Re}\,\beta >0.\end{array}\) 
